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 A294444 Number of distinct numbers appearing as denominators in row n of Kepler's triangle A294442. 2
 1, 1, 1, 2, 3, 6, 10, 16, 29, 51, 83, 148, 246, 402, 650, 1084, 1740, 2803, 4458 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS It would be nice to have a formula or recurrence. LINKS EXAMPLE Row 4 of A294442 contains eight fractions, 1/5, 4/5, 3/7, 4/7, 2/7, 2/7, 3/8, 5/8. There are three distinct denominators, so a(4) = 3. MAPLE # S[n] is the list of fractions, written as pairs [i, j], in row n of Kepler's triangle; nc is the number of distinct numerators, and dc the number of distinct denominators S[0]:=[[1, 1]]; S[1]:=[[1, 2]]; nc:=[1, 1]; dc:=[1, 1]; for n from 2 to 18 do S[n]:=[]; for k from 1 to nops(S[n-1]) do t1:=S[n-1][k]; a:=[t1[1], t1[1]+t1[2]]; b:=[t1[2], t1[1]+t1[2]]; S[n]:=[op(S[n]), a, b]; od: listn:={}; for k from 1 to nops(S[n]) do listn:={op(listn), S[n][k][1]}; od: c:=nops(listn);  nc:=[op(nc), c]; listd:={}; for k from 1 to nops(S[n]) do listd:={op(listd), S[n][k][2]}; od: c:=nops(listd);  dc:=[op(dc), c]; od: nc; # A294443 dc; # A294444 CROSSREFS Cf. A294442, A294443. See A293160 for a similar sequence related to the Stern-Brocot triangle A002487. Sequence in context: A034419 A201864 A198200 * A066895 A105075 A140669 Adjacent sequences:  A294441 A294442 A294443 * A294445 A294446 A294447 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Nov 20 2017 STATUS approved

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Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)